Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-09-29
Grav.Cosmol.16:118-125,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
14 pages, Latex, refs. are added, typos are eliminated
Scientific paper
10.1134/S0202289310020040
The (n +1)-dimensional Einstein-Gauss-Bonnet (EGB) model is considered. For diagonal cosmological metrics, the equations of motion are written as a set of Lagrange equations with the effective Lagrangian containing two "minisuperspace" metrics on R^n: a 2-metric of pseudo-Euclidean signature and a Finslerian 4-metric proportional to the n-dimensional Berwald-Moor 4-metric. For the case of the "pure" Gauss-Bonnet model, two exact solutions are presented, those with power-law and exponential dependences of the scale factors (w.r.t. the synchronous time variable). (The power-law solution was considered earlier by N. Deruelle, A. Toporensky, P. Tretyakov, and S. Pavluchenko.) In the case of EGB cosmology, it is shown that for any non-trivial solution with an exponential dependence of scale factors, a_i(\tau) = A_i exp(v^i \tau), there are no more than three different numbers among v^1, ..., v^n.
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